Title

Constructions of small symplectic 4-manifolds using luttinger surgery

Document Type

Article

Publication Date

1-1-2009

Abstract

Luttinger surgery is used to produce minimal symplectic 4- manifolds with small Euler characteristics. We construct a minimal symplectic 4-manifold which is homeomorphic but not diffeomorphic to ℂℙ #3ℂℙ , and which contains a genus two symplectic surface with trivial normal bundle and simply-connected complement. We also construct a minimal symplectic 4-manifold which is homeomorphic but not diffeomorphic to 3ℂℙ #5ℂℙ , and which contains two disjoint essential Lagrangian tori such that the complement of the union of the tori is simply-connected. These examples are used to construct minimal symplectic manifolds with Euler characteristic 6 and fundamental group ℤ, Zℤ , or ℤ/p ⊕ ℤ/q ⊕ ℤ/r for integers p, q, r. Given a group G presented with g generators and r relations, a symplectic 4-manifold with fundamental group G and Euler characteristic 10 + 6(g + r) is constructed. © 2009 Applied Probability Trust. 2 ¯ 2 2 ¯ 2 3

Publication Source (Journal or Book title)

Journal of Differential Geometry

First Page

317

Last Page

361

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